ひずみ勾配弾性理論を用いた共鳴振動現象のサイズ依存性解析

抄録

This study investigates the size-dependence of normal mode vibrations of an isotropic first strain gradient elasticity of Cauchy type. The elastic medium has a two-dimensional rectangular shape with the dimensions of L₁ = 1.1ξ and L₂ = 0.9ξ, where ξ is a scaling factor. Lagrangian density includes two kinds of length parameters, d and g, and which control the phonon dispersion relations. Numerical analysis conucted by the Ritz method revealed that the vibration frequencies follow the classical scaling law when the size of the medium is sufficiently large. On the other hand, however, notable deviations from the scaling law are observed below ξ < 5, irrespective to the symmetry of vibration. These results demonstrate that phonon dispersion is responsible for the emergence of size-effect in the normal mode vibrations.